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Yes the Mariner laments his loneliness using all kinds of poetic devices. We get that he is alone,

“Alone, alone, all, all alone, alone on a wide sea!”

He keeps reminding us of his loneliness using metaphor, personification, simile....

"I closed my lids, and kept them close, Till the balls like pulses beat; For the sky and the sea, and the sea and the sky. Lay like a load on my weary eye, And the dead were at my feet."

Coleridge also uses foreboding alliteration to get across his sense of isolation,

"Drop down the breeze, the sails dropped down, 'Twas sad as sad could be; and we did speak only to break the Silence of the sea!"

If that isn't enough there is this famous line of desperation,

"Water, water, every where, And all the boards did shrink: Water, water, every where, nor any drop to drink."

The Mariner seems like a lonely guy at the beginning of the poem. He corners unsuspecting wedding guests and creeps them out with his story that seems to go on forever. He seems used to it though. His BFF in the story is actually a hermit so you get the idea. The whole experience has left this guy wandering the sea-side looking for lost souls to tell his story to. Isolation and loneliness is his penance. I suppose anything looks better than hanging out with a ship full of dead men. At least he might get left overs at the wedding buffet.